Calculating ProbabilitiesCalculating Probabilities

Teach GCSE Maths

What is the probability that the bus is on time ?

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Calculating Calculating ProbabilitiesProbabilitiesCalculating Calculating

ProbabilitiesProbabilities

e.g. The probability that a bus arrives early is 0·1.The probability it arrives late is

0·5.What is the probability that the bus is on time ?Solution

: If the bus is on time, it cannot be early or late. These three events are mutually

exclusive.This just means that if one happens the others cannot.

e.g. The probability that a bus arrives early is 0·1.The probability it arrives late is

0·5.What is the probability that the bus is on time ?Solution

: If the bus is on time, it cannot be early or late.

The sum of all three probabilities is 1, so

The probability of being early or late

the probability of being on time = 1 0·6

= 0·1 + 0·5 = 0·6

= 0·4

e.g. A packet contains mixed sweet pea seeds. Each seed gives a plant with one of 5 colours of flowers.

Colour Red Pink Mauve White Magenta

Probability 0·2 0·15 0·25 0·1

The probabilities of 4 of the colours are shown below.

(a) What is the probability of a getting a plant with white flowers ?

(b)Find the probability of getting a plant which does not have red flowers.

A seed is taken out at random and planted.

Colour Red Pink Mauve White Magenta

Probability 0·2 0·15 0·25 0·1

The sum of the probabilities shown

=

(a) What is the probability of a getting a plant with white flowers ?

Solution:

= 0·7

0·20·150·250·10·70

0·2 + 0·15 + 0·25 + 0·1

The probability that the plant has white flowers

=1 0·7

= 0·3

0

0

Colour Red Pink Mauve White Magenta

Probability 0·2 0·15 0·25 0·1

Solution: The probability of not getting red

flowers = 1 the probability of red flowers= 1 0·2

0·3

(b)Find the probability of getting a plant which does not have red flowers.

= 0·8

What is the probability of scoring a 1 or a 2 ?

Suppose we have a triangular spinner that is equally likely to show the numbers 1, 2 and 3.

2

3

1

Decide with your partner what the probability, p, is of getting a 3 .

Ans: p = 13

Ans: 23

the probability of NOT getting a 3 = 1 - the probability of getting a 3

The probability of getting a 1 or 2 is the same as the probability of not getting a 3. So,

It is always true that the probability of an event not happening 1 the probability that

it happens.

e.g. When I throw a dice there are six outcomes.

The probability of a 6 on a fair dice is

Some games start when you throw a 6. 1

6If the probability of not getting a 6 is p, then 1 1

6

6= 66

1

56=

p =

SUMMARY

The probability that an event does NOT happen

= 1 p, where p is the probability that it does happen.

Events that are mutually exclusive cannot happen together. If one event occurs the others cannot. We find the probability of one of the mutually exclusive events by subtracting the sum of the other probabilities from 1.

1. The table gives the probabilities of a loaded( unfair) dice showing each of five of its faces.Number on face 1 2 3 4 5 6

Probability 0·3 0·15 0·15 0·15 0·1(a) Find the probability that the dice

shows a 3.(b) What is the probability that the dice does not show a 6 ?

Exercise

Number on face 1 2 3 4 5 6

Probability 0·3 0·15 0·15 0·15 0·1(a) Find the probability that the dice

shows a 3.

(b) What is the probability that the dice does not show a 6 ?

Solution:

The sum of the probabilities we are given is 0·3 + 0·15 + 0·15 + 0·15 + 0·1 = 0·85

The total probability is 1.So, the probability of a 3 is 1 0·85 = 0·15

The probability of not having a 6 = 1 the probability of having a

6= 1 0·1 = 0·9

0·15

2. A mixed netball match is played between a team of students and a team of their teachers.

The table shows the probabilities of the next goal being scored by particular types of players.

Player Prob.

A female teacher 0·1

A student 0·7

Calculate the probability that (a) the next goal is not scored by a teacher,

and(b)the next goal is scored by a male teacher.

Solution:

The probability that a student scores the goal = 0·7If the goal is not scored by a student, it must

be scored by a teacher

(a) Calculate the probability that the next goal is not scored by a teacher.

so, the probability of a teacher scoring the goal

= 1 – 0·7 = 0·3

Player Prob.

A female teacher 0·1

A student 0·7

2. A mixed netball match is played between a team of students and a team of their teachers.

Solution:

We have just found that the probability of a teacher scoring the goal = 0·3

Player Prob.

A female teacher

A student

(b)Calculate the probability that the next goal is scored by a male teacher.

The probability that it is a female teacher is 0·1 so, the probability that it is a male teacher

= 0·3 0·1 = 0·2

2. A mixed netball match is played between a team of students and a team of their teachers.

EITHER

0·1 0·1

0·7

Solution:

Player Prob.

A female teacher

A student

(b)Calculate the probability that the next goal is scored by a male teacher.

2. A mixed netball match is played between a team of students and a team of their teachers.

OR

The probability that a female teacher or a student scores the goal

= 0·8 so, the probability that a male teacher

scores the goal = 1 0·8 = 0·2

0·1

= 0·1 0·7

0·7

0·1

0·7